11.1 Electromagnetism

11.1 Electromagnetism

Quick Answer: Electromagnetism is the physics of charges, currents, and the fields they produce. For the PAF GD Pilot initial test you must know Coulomb's law, the electric field, electric flux (Phi = E S cos theta), Ohm's law, series and parallel circuits, the magnetic field around a current, Faraday's law of induction, and how transformers, motors, and generators work.

Electromagnetism is the single largest classical-physics topic on the PAF GD Pilot initial test because it underpins every aircraft electrical system, from the magneto that fires the spark plugs to the alternator that charges the battery. The Pakistan Air Force expects FSc-level fluency: you should be able to manipulate the formulas, predict the direction of an induced current, and reason about a circuit from its schematic.

Electrostatics and Coulomb's Law

Two point charges exert a force on each other given by Coulomb's law:

F = k * q1 * q2 / r^2

where k = 9 x 10^9 N m^2/C^2 is Coulomb's constant, q1 and q2 are the charges in coulombs, and r is the separation in metres. Like charges repel; unlike charges attract. The force acts along the line joining the charges. Doubling the distance cuts the force by a factor of four.

The electric field E at a point is the force per unit positive test charge placed there: E = F/q, measured in N/C or V/m. A point charge Q produces a field E = kQ/r^2 radially outward (for Q > 0).

Electric Flux

Electric flux measures how many electric field lines pass through a surface:

Phi = E * S * cos(theta)

where E is the field magnitude, S is the area of the surface, and theta is the angle between the field direction and the normal (perpendicular) to the surface. Flux is maximum when the surface is perpendicular to the field (theta = 0, cos theta = 1) and zero when the surface is parallel to the field (theta = 90 deg, cos theta = 0). Gauss's law builds on this idea: the net flux through a closed surface equals the enclosed charge divided by epsilon_0.

Worked Example: Flux Through a Wing Panel

An aircraft skin panel of area 0.50 m^2 sits in a 200 N/C electric field. If the panel's normal makes 60 deg with the field, the flux is Phi = 200 x 0.50 x cos(60 deg) = 200 x 0.50 x 0.5 = 50 N m^2/C. Rotating the panel to be perpendicular (theta = 0) doubles the flux to 100 N m^2/C.

Ohm's Law and DC Circuits

Ohm's law states that for a linear conductor at constant temperature, the current I is proportional to the potential difference V:

V = I * R

with V in volts, I in amperes, and R in ohms (omega). Power dissipated is P = VI = I^2 R = V^2/R.

Series and Parallel Resistors

For two resistors in parallel the handy form is Rp = R1*R2 / (R1 + R2). Adding resistors in series always increases total resistance; adding resistors in parallel always decreases it.

Worked Example: Circuit on a Light Bar

Two navigation-light resistors, 6 ohm and 3 ohm, are connected in parallel across a 12 V bus. The equivalent resistance is Rp = 6*3/(6+3) = 18/9 = 2 ohm. Total current drawn from the bus is I = V/Rp = 12/2 = 6 A. The 3 ohm branch carries 12/3 = 4 A and the 6 ohm branch carries 12/6 = 2 A, summing to 6 A as required.

Magnetic Field from a Current

A current-carrying conductor produces a magnetic field around it. For a long straight wire the magnitude at distance r is:

B = (mu_0 * I) / (2 * pi * r)

where mu_0 = 4 pi x 10^-7 T m/A is the permeability of free space. The right-hand grip rule gives the direction: thumb along the conventional current, fingers curl in the direction of B. A solenoid produces a nearly uniform field inside, B = mu_0 * n * I, where n is turns per metre.

A charge q moving with velocity v in a field B feels the Lorentz force F = q v B sin(theta), perpendicular to both v and B. This is the principle behind the cathode-ray tube and the mass spectrometer.

Faraday's Law of Electromagnetic Induction

Faraday's law states that a changing magnetic flux through a loop induces an electromotive force (EMF):

EMF = -N * (dPhi / dt)

where N is the number of turns and the minus sign is Lenz's law: the induced current always opposes the change that produced it. This is the operating principle of generators, transformers, and ignition coils.

A conductor of length L moving at speed v perpendicular to a field B has motional EMF = B L v. Aircraft magnetos use this: a rotating magnet spinning past a coil induces the high-voltage pulse that fires each spark plug.

Transformers

A transformer transfers electrical energy between two circuits by mutual induction. It has a primary coil of Np turns and a secondary coil of Ns turns wound on a common iron core. For an ideal transformer (100% efficient, no losses):

Vp / Vs = Np / Ns      and      Ip / Is = Ns / Np

A step-up transformer has Ns > Np and raises voltage; a step-down transformer has Ns < Np and lowers voltage. Transformers only work with alternating current because a steady DC produces no changing flux and hence no induced EMF in the secondary. They operate entirely on Faraday's law.

Worked Example: Step-Down Transformer

An aircraft transformer has 2400 primary turns and 120 secondary turns. If the primary is driven at 240 V AC, the secondary voltage is Vs = Vp * (Ns/Np) = 240 * (120/2400) = 240 * 0.05 = 12 V AC, suitable for avionics lighting. The secondary current available is 20 times the primary current, reflecting power conservation.

Motors and Generators

A DC motor converts electrical energy into mechanical rotation: current in a coil placed in a magnetic field experiences a torque that spins the shaft. A generator does the reverse: mechanical rotation of a coil in a field induces an EMF via Faraday's law. The aircraft alternator is a generator driven by the engine; it supplies the DC bus through a rectifier.

Aviation Link

Every light aircraft has a magneto per cylinder: a self-contained magneto-generator that needs no battery. Spinning the magnet changes flux through the coil, Faraday's law induces a high voltage, and the spark ignites the fuel-air mixture. Understanding this chain is why PAF examiners test induction so heavily.